How to use logarithm to solve for x?
Can someone please explain to me how to do from question e onwards? Thanks!
Can someone please explain to me how to do from question e onwards? Thanks!
2 Answers
Each of these log questions are written in the form
For example, let's take
Explanation:
(e)(e)
"using the "color(blue)"laws of logarithms"using the laws of logarithms
•color(white)(x)logx^nhArrnlogx∙xlogxn⇔nlogx
•color(white)(x)log_b b=1∙xlogbb=1
"given "10^x=110given 10x=110
"take " log_(10)" of both sides"take log10 of both sides
rArrlog_(10)10^x=log_(10)110⇒log1010x=log10110
rArrxcancel(log_(10)10)^1=log_(10)(11xx10)
rArrx=log_(10)10+log_(10)11
rArrx=1+log_(10)11